The present invention relates to equalization techniques to compensate for channel transmission distortion in digital communication systems. In particular, the present invention relates to the efficient baseband and passband implementations of the Constant Modulus Algorithm (CMA), an equalization algorithm used in blind equalization systems.
Digital transmission of information typically involves the modulation of pulses onto an RF carrier""s amplitude and/or phase. Most propagation mediums (terrestrial, cable, underwater, etc.) introduce signal distortion. Factors that cause distortions include noise, signal strength variations, phase shift variations, multiple path delays, and the like.
Noise is also known as static. Signal strength variations are commonly known as fading. In addition, multiple different paths between the transmitter and receiver through the propagation medium cause multiple path delays. The different paths have different delays that cause replicas of the same signal to arrive at different times at the receiver (like an echo). Multi-path distortion results in inter-symbol interference (ISI) in which weighted contributions of other symbols are added to the current symbol.
In addition to distortion and noise from the propagation medium, front-end portions of the receiver and transmitter also introduce distortion and noise. The presence of distortion, noise, fading and multi-path introduced by the overall communication channel (transmitter, receiver and propagation medium), can cause digital systems to degrade or fail completely when the bit error rate exceeds some threshold and overcomes the error tolerance of the system.
Digital systems transmit data as symbols having discrete levels of amplitude and/or phase. To the extent that a symbol is received at a level that differs from one of the allowed discrete levels, a measure of communication channel error can be detected. At the receiver, it is known to use an equalizer responsive to the detected error to mitigate the signal corruption introduced by the communications channel. It is not uncommon for the equalizer portion of a receiver integrated circuit to be over half of the integrated circuit area.
An equalizer is a filter that has the inverse characteristics of the communication channel. If the transmission characteristics of the communication channel are known or measured, then the equalization filter parameters can be set directly. After adjustment of the equalization filter parameters, the received signal is passed through the equalizer, which compensates for the non-ideal communication channel by introducing compensating xe2x80x9cdistortionsxe2x80x9d into the received signal which tend to cancel the distortions introduced by the communication channel.
However, in most situations such as in broadcasting, each receiver is in a unique location with respect to the transmitter. Accordingly, the characteristics of the communication channel are not known in advance, and may even change with time. In those situations where the communication channel is not characterized in advance, or changes with time, an adaptive equalizer is used. An adaptive equalizer has variable parameters that are calculated at the receiver. The problem to be solved in an adaptive equalizer is how to adjust the equalizer filter parameters in order to restore signal quality to a performance level that is acceptable by subsequent error correction decoding.
In some adaptive equalization systems, the parameters of the equalization filter are set using a predetermined pilot signal (a training sequence), which is periodically sent from the transmitter to the receiver. The received training sequence is compared with the known training sequence to derive the parameters of the equalization filter. After several iterations of parameter settings derived from successive training sequences, the equalization filter converges to a setting that tends to compensate for the distortion characteristics of the communications channel.
In blind equalization systems, the equalizer filter parameters are derived from the received signal itself without using a training sequence. In the prior art, it is known to adjust the equalizer parameters blindly using the Least Mean Squares (LMS) algorithm, in which the training symbols are replaced with hard decisions, or best estimates of the original input symbols. Blind equalization systems using LMS in this manner are referred to as Decision Directed LMS (DD-LMS).
However, the DD-LMS algorithm requires a good initial estimate of the input signal. For most realistic communication channel conditions, the lack of an initial signal estimate results in high decision error rates, which cause the successively calculated equalizer filter parameters to continue to fluctuate, rather than converge to a desired solution. The parameters are set to diverge in such case.
It is also known to use another algorithm, called the Constant Modulus Algorithm (CMA), in combination with the DD-LMS algorithm from a cold start. See D. N. Godard, xe2x80x9cSelf-recovering equalization and carrier tracking in two-dimensional data communication systems,xe2x80x9d IEEE Transactions on Communications, vol. 28, no 11, pp. 1867-1875, October 1980, or J. R. Treichler, B. G. Agee, An New Approach To Muli-Path Correction Of Constant Modulus Signals, IEEE Transactions On Acoustics Speech And Signal Processing, vol ASSP-31, no. 2, page 459-472 April 1983. The CMA algorithm is used first to calculate the equalizer filter parameters, which is regarded as an initial estimate. Thereafter, the equalizer filter parameters (as calculated by the CMA algorithm) are used in an acquisition mode to find the initial equalizer filter parameters to start the DD-LMS algorithm.
The CMA algorithm (as well as the DD-LMS algorithm) is usually implemented with a gradient descent strategy in which the equalizer parameters are adapted by replacing the present equalizer parameter settings with their current values plus an error (or correction) term. See C. R. Johnson, Jr., P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R. A. Casas, xe2x80x9cBlind equalization using the constant modulus criterion: a review,xe2x80x9d Proceedings of the IEEE, vol. 86, no. 10, pp. 1927-1950, October, 1998.
From a cold start, the receiver enters an acquisition mode. In the acquisition mode, the CMA algorithm is used first to adjust the equalizer parameters. Then, after a fixed period of time (or alternatively from a measure derived from the equalizer output), the receiver switches to the DD-LMS algorithm in a tracking mode. The acquisition mode typically requires up to 400,000 symbols. At a 10 MHz clock rate, the symbol rate is 100 nanoseconds and the time available for acquisition using the CMA algorithm is about 40 milliseconds. Overall, between the initial CMA algorithm and the following DD-LMS algorithm, the equalizer has about 100-200 milliseconds to converge.
A critical factor in an adaptive equalization system is to complete all the required multiplication operations within the time available: i.e., a single symbol interval. In particular, the error term calculation requires successive multiply operations for each equalizer parameter. One multiply per equalizer parameter is needed for one-dimensional signaling, and two multiplies per equalizer parameter is needed for two-dimensional signaling. Since a typical equalizer filter may have up to 512 filter coefficients (the number of equalizer filter parameters), the total time required to complete all the required multiplication operations with full precision often exceeds one symbol interval. That is, the large number of multiply operations often takes so long that the total time needed for calculation of all the equalizer filter coefficients exceeds the available time limit of one symbol interval. Thus, although the prior art scheme to use CMA and DD-LMS in series is theoretically possible, the large number of multiply operations prevents practical, economical commercial implementations in reasonably sized integrated circuit components. In the preferred embodiment the large number of multiply operations will be replaced with programmable shifts and adders which values are determined using a lookup table.
One prior art solution to the problem of economical implementation includes calculating subsets of the equalizer filter coefficients in successive symbol intervals. Another prior art approach is to simplify one term of the multiplication (in this case, the error term) by using only the sign of the error term, i.e., +1 or xe2x88x921. In LMS, this variation is referred to as signed-error LMS (SE-LMS) in which the usual LMS error term is replaced by the sign (+/xe2x88x921) of the error. SE-LMS is easily implemented since the usual multiplier per equalizer parameter in the LMS update equation is replaced by a simple bit flip (a sign change) to represent multiplication by +1 or xe2x88x921. Similarly, in CMA a signed-error CMA (SE-CMA), is used to replace the usual, full precision CMA error term with its sign (+1 or xe2x88x921). Since multiplication by +1 or xe2x88x921 is just a sign change, multiply calculations are very rapid. A modification of the signed error approach is to use three levels, +1, 0, xe2x88x921 for the error term in the multiplication. Since the number 0 is neither positive nor negative, multiplication by +1, 0, xe2x88x921 is still a simple and quick operation. However, approximating a term by its sign sacrifices accuracy and can increase the time required for the adaptive equalizer to converge to a solution. Furthermore, convergence is not guaranteed.
The present invention is embodied in a blind equalization system in which the error quantizer used to digitize the CMA error function uses different quantization levels in different regions of the CMA error function. The use of different quantization levels in different regions increases quantization precision in area of the CMA error function typically encountered when the equalizer parameters are near convergence.
In another embodiment of the present invention, a quantizer with a step rise having logarithmic scale is used to digitize the CMA error function. In particular, a quantizer with a step rise in which each level of the quantizer step rise is a power of 2 is used to digitize the CMA error function. The use of a power of 2 for the quantizer step rise size simplifies multiplication since multiplication by a power of 2 is a shift operation.
In yet another embodiment of the present invention, a quantizer with a step rise in which each level of the quantizer step rise is the sum of two or more logarithmic scales is used to digitize the CMA error function. In particular, a quantizer with a step rise wherein each level of the quantizer step rise is the sum of two or more numbers each of which is a power of 2, is used to digitize the CMA error function. The use of the sum of two numbers, each of which is a power of 2 for the quantizer step size rise simplifies multiplication since shift and addition operations thus achieve multiplication.